Has a customer ever used a major incident or outage to bargain or secure a better deal from your business? Is there any way to turn this negative situation into a positive?

Unfortunately, these types of incidents seem to occur from time to time, and they can have a significant impact on a business. However, it's important to note that Service Level Agreements (SLAs) are in place to help mitigate losses, covering them to the extent outlined in the agreement. Beyond that, it's crucial to focus on rebuilding trust through goodwill efforts. There are several ways to approach this, such as offering short-term discounts on services until everything is fully restored or providing a dedicated 24-hour support team to address immediate concerns. The ultimate goal is for the customer to feel that the issue has been resolved and that it is "business as usual." It is essential to highlight the support they received and the vendor's efforts in overcoming the situation, turning a negative experience into a positive one. These actions help shift the narrative and reinforce the commitment to customer satisfaction.

Hi, writing from perspective of a vendor and SaaS provider.
Situation 1:
It happened to us that contracted data centre where we were hosting hundreds of clients burned out completely. Big fire, the event took attention of media as impacted numerous business.
Now, as we were able to restore clients just next day before noon and explaining the root cause we received actually very positive feedbacks at the end of the day. Only few complains.
Curtail point was to inform clients immediately about nature of problem, steps we are making proactively and realistic expectation about problem solved. So clients were not left in the dark about what's going on and when the service will be online again. I believe that is the example that problem solved strengthen the relationship.

Situation 2: yes it also happened to us,  that we made  operational mistake caused unavailability of service, again rather temporarily. In similar cases I recommend to proactively provide and execute some subscription time for free or other valuable service which may not cost the provider extensive cost, but bring value to client. That may prevent unpleasant and expensive talks. Again early information and progress update is crucial to minimize reputation damage.
In some cases such negative situation turned to success, that client realize that provided system is critical for operations. That lead even to upsell to enterprise services like individual backups, dedicated servers, SLA, High availability solutions.. 

To summarize:
- have clients well segmented and your business continuity plan reflects your commitments and segmentation. Big clients or clients with SLA and enterprise services goes first.
- Inform clients actively, so your support is not overloaded by questions and can focus on problem resolution. It is better to let clients know that they will be off for a day rather than miss optimistic resolution time. It minimize the frustration at the end. Promise delivered.
- Deliver something if relevant and possible - avoid as many individual complains resolution as possible.

I have had this happen two ways; the # 1 issue was due to the vendor, and then I put everything back to the vendor to ensure the client was happy.  It was never an issue and the client always appreciated the vendor more, building a stronger relationship. # 2 The customer has a discussion and demo with us, and they decide to go in another direction.  It fails, and they attempt to see if we can give them a much higher discount to offset their mistake.